StackOverflow2013

Note that there are some explanatory texts on larger screens.

plurals

PO
primarykey
Id
13102103
data
AcceptedAnswerId
0
AnswerCount
0
ClosedDate
CommentCount
0
CommunityOwnedDate
CreationDate
2012-10-27T16:44:15.040
FavoriteCount
0
LastActivityDate
2012-10-27T16:44:15.040
LastEditDate
LastEditorUserId
0
OwnerUserId
5852
ParentId
12963733
PostTypeId
2
Score
12
ViewCount
0
LastEditorDisplayName
text
Body
One more try, inspired by pigworkers post and <a href="http://hackage.haskell.org/packages/archive/representable-functors/3.0.0.1/doc/html/Data-Functor-Representable.html" rel="noreferrer">http://hackage.haskell.org/packages/archive/representable-functors/3.0.0.1/doc/html/Data-Functor-Representable.html</a>. A representable (or Naperian) functor is a comonad itself, if the key (or log) is a monoid! Then <code>coreturn</code> gets the value at position <code>mempty</code>. And <code>cojoin</code> <code>mappend</code>s the two keys it has available. (Just as the comonad instance for <code>(p ->)</code>.) <pre><code>{-# LANGUAGE KindSignatures #-} {-# LANGUAGE DataKinds #-} {-# LANGUAGE GADTs #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE UndecidableInstances #-} import Data.List (genericIndex) import Data.Monoid import Data.Key import Data.Functor.Representable data Nat = Z | S Nat data U (n :: Nat) x where Point :: x -> U Z x Dimension :: [U n x] -> U n x -> [U n x] -> U (S n) x dmap :: (U n x -> U m r) -> U (S n) x -> U (S m) r dmap f (Dimension ls mid rs) = Dimension (map f ls) (f mid) (map f rs) instance Functor (U n) where fmap f (Point x) = Point (f x) fmap f d@Dimension{} = dmap (fmap f) d class Functor w => Comonad w where (=>>) :: w a -> (w a -> b) -> w b coreturn :: w a -> a cojoin :: w a -> w (w a) x =>> f = fmap f (cojoin x) cojoin xx = xx =>> id </code></pre> <code>U</code> is representable if the lists are infinitely long. Then there's only one shape. The key of <code>U n</code> is a vector of n integers. <pre><code>type instance Key (U n) = UKey n data UKey (n :: Nat) where P :: UKey Z D :: Integer -> UKey n -> UKey (S n) instance Lookup (U n) where lookup = lookupDefault instance Indexable (U n) where index (Point x) P = x index (Dimension ls mid rs) (D i k) | i < 0 = index (ls `genericIndex` (-i - 1)) k | i > 0 = index (rs `genericIndex` ( i - 1)) k | otherwise = index mid k </code></pre> We need to split the <code>Representable</code> instance up in two cases, one for <code>Z</code> and one for <code>S</code>, because we don't have a value of type <code>U n</code> to pattern match on. <pre><code>instance Representable (U Z) where tabulate f = Point (f P) instance Representable (U n) => Representable (U (S n)) where tabulate f = Dimension (map (\i -> tabulate (f . D (-i))) [1..]) (tabulate (f . D 0)) (map (\i -> tabulate (f . D i)) [1..]) instance Monoid (UKey Z) where mempty = P mappend P P = P instance Monoid (UKey n) => Monoid (UKey (S n)) where mempty = D 0 mempty mappend (D il kl) (D ir kr) = D (il + ir) (mappend kl kr) </code></pre> And the key of <code>U n</code> is indeed a monoid, so we can turn <code>U n</code> into a comonad, using the default implementations from the representable-functor package. <pre><code>instance (Monoid (UKey n), Representable (U n)) => Comonad (U n) where coreturn = extractRep cojoin = duplicateRep (=>>) = flip extendRep </code></pre> This time I did some testing. <pre><code>testVal :: U (S (S Z)) Int testVal = Dimension (repeat (Dimension (repeat (Point 1)) (Point 2) (repeat (Point 3)))) (Dimension (repeat (Point 4)) (Point 5) (repeat (Point 6))) (repeat (Dimension (repeat (Point 7)) (Point 8) (repeat (Point 9)))) -- Hacky Eq instance, just for testing instance Eq x => Eq (U n x) where Point a == Point b = a == b Dimension la a ra == Dimension lb b rb = take 3 la == take 3 lb && a == b && take 3 ra == take 3 rb instance Show x => Show (U n x) where show (Point x) = "(Point " ++ show x ++ ")" show (Dimension l a r) = "(Dimension " ++ show (take 2 l) ++ " " ++ show a ++ " " ++ show (take 2 r) ++ ")" test = coreturn (cojoin testVal) == testVal && fmap coreturn (cojoin testVal) == testVal && cojoin (cojoin testVal) == fmap cojoin (cojoin testVal) </code></pre>
Tags
Title
singulars
PostAcceptedAnswerId
1. This table or related slice is empty.
PostParentId
1. POWriting cojoin or cobind for n-dimensional grid type
 singulars
 PostTypePostTypeId
 PTQuestion
PostTypePostTypeId
1. PTAnswer
UserLastEditorUserId
1. This table or related slice is empty.
UserOwnerUserId
1. USSjoerd Visscher
plurals
PostLinksPostIdRelatedPostId
1. This table or related slice is empty.
PostLinksRelatedPostIdPostId
1. This table or related slice is empty.
PostsAcceptedAnswerId
1. This table or related slice is empty.
PostsParentIdCreationDate
1. This table or related slice is empty.
VotesPostIdCreationDate
1. VO
 singulars
 PostPostId
 PO
 UserUserId
 This table or related slice is empty.
 VoteTypeVoteTypeId
 VTUpMod
2. VO
 singulars
 PostPostId
 PO
 UserUserId
 This table or related slice is empty.
 VoteTypeVoteTypeId
 VTUpMod
3. VO
 singulars
 PostPostId
 PO
 UserUserId
 This table or related slice is empty.
 VoteTypeVoteTypeId
 VTUpMod
CommentsPostId
1. This table or related slice is empty.

Querying!

Guidance

A row detail

Detail views are divided into sections. All the information in the data section comes from columns in the selected row. The other sections display data from other, related rows.

Related data can be related in a to-one or a to-many fashion. Captions of data related in a to-many fashion link to a list view showing a filtered view of the table.

Try moving around until you find a non-empty to-many entry and click on the label to get to one. You can move back to the root by clicking on the database name in the header.